Conclusion in the framework of nonextensive kinetics of the Jeans instability criterion for protoplanetary cloud taking into account radiation and magnetic field.

In the framework of Tsallis statistics, we study the effect nonintensity of medium on the Jeans gravitational instability criterion for a self-gravitating protoplanetary cloud, the substance of which consists of a mixture of ideal $q$-gas and blackbody radiation. The generalized criteria for Jeans's gravitational instability are found from the corresponding dispersion relations obtained for both neutral matter and plasma. A generalized integral Chandrasekhar stability criterion for a gravitating spherical cloud is also obtained. The presented results are analyzed for various values of the deformation parameters $q$, the fractional dimension $D$ of the velocity space and the coefficient $\beta$, characterizing the fraction of radiation in the total pressure of the system. It is shown that radiation can stabilize the considered nonextensive pure gas systems, and for a plasma the Jeans instability criterion is modified by the magnetic field and radiation pressure only in the transverse mode of propagation of the perturbation wave.